timeline of calculus

Calculus was developed as a way to calculate areas and volumes of shapes that are not easy to figure using simple math. Differential calculus studies the derivative, which calculates the slope of a line tangent to the function. The slope of the line shows the rate of change in the line. If the line represents velocity, the slope shows the change in velocity, or acceleration.

Integral calculus studies the “anti-derivative”, which calculates the original function from a derivative. Integrals can be used to calculate the area under a curve, which can represent area or volume of a curved shape or other complex problems such as speed/time calculations with a variable speed component.

The “fundamental theorem of calculus” states that derivatives and integrals and the processes associated with finding them are essentially the inverse of each other. This concept was developed simultaneously and independently by both Newton and Leibniz.

-1820 – Moscow papyrus, calculations of volume – Egypt
-0450 – problems based on infinity – Zeno (of Elea)
-0370 – method of exhaustion – Eudoxus and Antiphon
-0225 – first known summation of an infinite series – Archimedes
0263 – Cavalieri’s principle (“Nine Chapters”) – Liu Hui
0499 – trigonometry and sum of cubes (volume) – Aryabhata
1021 – Alhazen’s problem (“Book of Optics”), integrals of fourth degree – Alhazen
1150 – spherical trigonometry and Rolle’s theorem – Bhaskara
1400 – infinite series expansions – Madhava
1615 – infinitesimally small geometric quantities – Kepler
1635 – theory of indivisibles – Cavalieri
16xx – motion with variable speed – Torricelli and Barrow
1679 – maxima, minima and tangents – Fermat
1684 – infinitesimal calculus – Leibniz
1693 – fluxion calculus – Newton
1825 – integral theorem – Cauchy

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